Related papers: Variational Gaussian approximation for the magneti…
This paper is about the fractional Schr\"odinger equation expressed in terms of the Caputo time-fractional and quantum Riesz-Feller space fractional derivatives for particle moving in a potential field. The cases of free particle (zero…
We propose a time fractional extension of the Schr{\"o}dinger equation that keeps the main mechanical and quantum properties of the classical Schr{\"o}dinger equation. This extension is shown to be equivalent to another well identified time…
The linear Schr\"odinger equation with piecewise constant potential in one spatial dimension is a well-studied textbook problem. It is one of only a few solvable models in quantum mechanics and shares many qualitative features with…
We show how the Laplace transform can be used to give a solution of the time-dependent Schr\"odinger equation for an arbitrary initial wave packet if the solution of the stationary equation is known. The solution is obtained without summing…
We take a closer and new look at the effects of tidal forces on the free fall of a quantum particle inside a spherically symmetric gravitational field. We derive the corresponding Schr\"odinger equation for the particle by starting from the…
We show that Liouville-von Neumann approach to quantum mechanical systems, which demands the existence of invariant operators, reproduces the time-dependent variational Gaussian approximation. We find the effective action of the…
We derive optimal order a posteriori error estimates for fully discrete approximations of linear Schr\"odinger-type equations, in the $L^\infty(L^2)-$norm. For the discretization in time we use the Crank-Nicolson method, while for the space…
In this paper we studied approximate solutions of the radial Schr\"odinger equation with the attractive Gaussian potential. We used asymptotic iteration method and variational method in order to obtain energy eigenvalues for any $n$ and $l$…
A simple and explicit technique for the numerical solution of the two-particle, time-dependent Schr\"{o}dinger equation is assembled and tested. The technique can handle interparticle potentials that are arbitrary functions of the…
We present Lagrangian which implies both necessary constraints and dynamical equations for position and spin of relativistic spin one-half particle. The model is consistent for any value of magnetic moment $\mu$ and for arbitrary…
We propose a method to describe the evolution of two spins coupled by hyperfine interaction in an external time-dependent magnetic field. We apply the approach to the case of hyperfine interaction with axial symmetry, which can be solved…
We discuss the dynamics of single particle by laying a hypothesis that the Hamilton's principle of stationary action is not exact. We then postulate that the deviation of the action with sufficiently short time interval from the stationary…
We consider the stochastic nonlinear Schroedinger equation driven by a multiplicative noise in a semiclassical regime, where the Plank constant is small. In this regime, the solution of the equation exhibits high-frequency oscillations. We…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…
We show that the Schr\"odinger equation can be derived assuming the Galilean covariance of a generic wave equation and the validity of the de Broglie's wave-particle duality hypothesis. We also obtain from this set of assumptions the…
Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the…
In this work, we extend the time-dependent conformable Schr\"odinger equation for a fractional dimensional system of N spatial coordinates to be used as an effective description of anisotropic and confined systems. A specific example is…
We construct an approximation of the kernel of the solution of the time dependent Schr\"odinger equation whose Hamiltonian is a 2D harmonic oscillator in Aharonov-Bohm magnetic field. The main tools used here were established in the paper…
A new type of solution for the full 3+1 dimensional space-time Schroedinger equation is presented here. We consider elegant presentation of the exact solution in a spherical coordinate system, along with the assuming of separation of the…
This paper addresses issues surrounding the concept of fractional quantum mechanics, related to lights propagation in inhomogeneous nonlinear media, specifically restricted to a so called gravitational optics. Besides Schr\"odinger Newton…